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Prove that for 0 < a < b < c cot^-1 (1...

Prove that for 0 < a < b < c
`cot^-1 (1+ab)/(a-b) + cot^-1 (1+bc)/(b-c) + cot^-1 (1+ca)/(c-a) = pi`

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PRADEEP PUBLICATION-INVERSE TRIGONOMETRIC FUNCTIONS-EXERCISE
  1. Solve the following equations. cos(tan^-1x) = sin (cot^-1 (3//4)

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  2. Solve the following equations: tan^-1(x+1) + tan^-1 (x-1) = tan^-1 (...

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  3. Prove that for 0 < a < b < c cot^-1 (1+ab)/(a-b) + cot^-1 (1+bc)/(b-...

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  4. If tan^-1x + tan^-1y + tan^-1z = pi, then prove that: x + y + z = xyz.

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  5. Find the value of the following: tan1/2[sin^-1(2x/(1+x^2)) + cos^-1(1-...

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  6. Prove that : tan^-1[(sqrt(1+x^2) - sqrt(1-x^2))/(sqrt1+x^2 + sqrt(1-x^...

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  7. Prove the following: cos[tan^-1{sin(cot^-1x)}]=sqrt((1+x^2)/(2+x^2))

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  8. If x in R, find the maximum and minimum values of 2 tan^-1 x + sin^-1 ...

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  9. Find the values of sec^-1( 2/sqrt3)

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  10. Find the values of sec^-1(Sec((4pi)/3))

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  11. Find the values of cot (cosec^-1 (-1))

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  12. Show that 2 tan^-1 x = cosec^-1((1+x^2)/(2x)), 0 < |x| le 1

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  13. Solve the equation cosec^-1(x/8) + cosec ^-1 (x/15) = pi/2

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  14. Solve the equation sec^-1(x/a) - sec^-1(x/b) = sec^-1b - sec^-1 a ...

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  15. Prove that cot^-1 x = cosec^-1 sqrt(1+x^2) for x ge 0

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  16. Prove that tan(sec^-1 x) = sqrt(x^2 - 1) for x le 1

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  17. Prove that cosec^-1 x = cot^-1sqrt(x^2 -1) for x ge 1

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  18. Prove that cot(cosec^-1x) = sqrt(x^2 - 1) for x ge 1

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  19. Prove that : sec^2 (tan^(-1)2) + cosec^2 (cot^(-1) 3) = 15

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  20. Find the values of tan^2 (Sec^-1 2) + cot^2 (cosec^-1 3)

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